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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,526

Hi;

Anyways, the asymptotic forms come in handy when you can not get an exact answer. The best part about them is that the larger the problem the more accurate they get!

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Yes, you are right.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,526

Hi gAr;

See you in a bit, got to do a chore.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Okay, see you later.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,526

It is obvious that there is no one way to get these.

A different method might be required each time...

Supposing we start with the GF:

We wish to get the an asymptotic form for the coefficients of z^n

The Wilf partial fraction:

That stumped me for a long time. Since I know Wilf uses maple

he should have at least shown the command that will do this.

He did not and till now I never figured it out.

By using z = {-2,-1,0,1,2,3} we can form the six equations we

need to achieve Wilf's partial fraction.

One of the solutions to this set of simultaneous equations is:

So

No simplifying done to preserve clarity and structure.

Now from expanding manually the coefficient of z^20 is -3968.24698980352. Try g(20)...

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,478

Hi bobbym,

The values are very close! Good one.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,526

Yes, because the denominator only has one real pole, subtracting it off

which is somehow done with his method. This greatly increases the convergence. The coefficients depend on the singularities of the g(x).

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,380

bobbym wrote:

Hi gAr;

You used the Knuth idea to get a smaller recurrence, very good. I am working

on a method that uses residues, it will take a while.

Knuth idea?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,526

Hi;

It is a Knuth idea that gAr and I were looking at for the gf of the coin problem.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,380

What is that Knuth idea?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,526

Hi;

I would suggest you get it straight from Knuth.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,380

Is it in a book?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,526

Yes, "Concrete Mathematics" Knuth, Graham and Patashnik.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,380

I will have to look at it.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,526

Do that right now! It is a very good book and you will find it interesting perhaps it will be your favorite.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,380

2nd edition?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,526

Yes, p345 on.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,380

Okay, I just needed to know if that is the one I need to find.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,526

Yes, 2nd edition get your copy while supplies last.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,380

I have.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,526

Very good. gAr likes it a little more than I do but we both like it.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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